1. ## nilpotent matrices

are all nilpotent matrices singular?
if so, how is that possible?

cheers

2. Originally Posted by the wildcat
are all nilpotent matrices singular?
if so, how is that possible?

cheers
Yes.

I quote from Nilpotent matrix - Wikipedia, the free encyclopedia:

"Over an algebraically closed field, a matrix M is nilpotent if and only if its eigenvalues are all zero. Therefore the determinant and trace of M are both zero, and nilpotent matrices are not invertible."